By straight line proportion (figure 92(b)) we can calculate the strain in
compression
steel when the extreme concrete fiber has a compressive strain of
0.003.
ε_{s}′ = ( x  d′ ) (0.003) / x =
(5.96  3) (0.003) / 5.96 = 0.00149
yield strain of steel, ε_{y} = f_{y}
/E_{s} = 40 / 29000 = 0.00138
ε_{s}′ is greater than ε_{y} ,
this means that compression steel has yielded before crushing of concrete,
hence the assumption is verified and the value of x is
valid.
If Compression steel does not yield; then ?? see
Example 93
Now we determine the strain in the two layers of tension steel.
Using strain diagram we can calculate the strain in tension steel
Lower most layer of tension steel
ε_{s1} = 0.003(25 + 0.5 + 1.28/2  5.96)
/ 5.96 = 0.01
Second layer of tension steel
ε_{s2} = 0.003(25  0.5  1.28/2  5.96) / 5.96 =
0.009
The strain in both the layers of tension steel is more than yield
strain and also greater than 0.005. Hence the section is tensioncontrolled.
The nominal flexural strength is computed as given below;
M_{n} = C_{c} (d  a/2) + C_{s}
(d  d′ )
= 263.54 (25  4.77/2) + 56.485
(25  3) = 7202.63
inkips
M_{n} = 600.22 ftkips
see another
problem 91 and
problem 93 on Reinforced Concrete
